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We use the representation theory of Lie algebras and computational linearalgebra to obtain an explicit formula for the hyperdeterminant of a $3 \times 3\times 2$ array: a homogeneous polynomial of degree 12 in 18 variables with16749 monomials and 41 distinct integer coefficients; the monomials belong to178 orbits under the action of $(S_3 \times S_3 \times S_2) \rtimes S_2$. Wealso obtain the simplest invariant for a $4 \times 4 \times 2$ array: ahomogeneous polynomial of degree 8 in 32 variables with 14148 monomials and 13distinct integer coefficients; the monomials belong to 28 orbits under $(S_4\times S_4 \times S_2) \rtimes S_2$.

The hyperdeterminant of 3 x 3 x 2 arrays, and the simplest invariant of 4 x 4 x 2 arrays